How do you write 5x^(4/9) in radical form?

Apr 27, 2017

See the solution process below:

Explanation:

First, we can use this rule of exponents to rewrite the expression:

${x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}} = {\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}}$

$5 {x}^{\frac{4}{9}} = 5 {x}^{\textcolor{red}{4} \times \textcolor{b l u e}{\frac{1}{9}}} = 5 {\left({x}^{\textcolor{red}{4}}\right)}^{\textcolor{b l u e}{\frac{1}{9}}}$

Now, we can use this rule of exponents to rewrite this expression in radical form:

${x}^{\frac{1}{\textcolor{red}{n}}} = \sqrt[\textcolor{red}{n}]{x}$

$5 {\left({x}^{4}\right)}^{\frac{1}{\textcolor{red}{9}}} = 5 \sqrt[\textcolor{red}{9}]{{x}^{4}}$